Suppose $Ax^2+Bxy+Cy^2+Dx+Ey+k=0$ is a conic in the Euclidean plane. How do I recognize what is it? In my book they have proved the determinant test that if $B^2-4AC$ is $>0$ if hyperbola, $=0$ if parabola and $<0$ if it is an ellipse.
But my confusion is that they do not include pair of straight lines and the circle(though it is a special case of the ellipse).